There are two completely different "wireless adapters" for Xbox 360. Which one do you need?
Purpose: Connect wireless Xbox 360 controllers to a Windows PC.
Purpose: Connect the Xbox 360 console to Wi-Fi (original "Fat" 360 lacks built-in Wi-Fi).
If you have a wired 360 controller and want it wireless on the console: Impossible. The console only talks to official wireless controllers. No adapter exists to make a wired controller wireless on the 360 itself.
On PC: Just plug the wired controller in via USB. It works natively.